AntisymmetricTensor.h File Reference

Basic algebra for antisymmetric 2nd order tensors. More...

#include "objects/geometry/SymmetricTensor.h"
#include "objects/containers/StaticArray.h"

Go to the source code of this file.

Classes
struct	PseudoVectorTag
class	AntisymmetricTensor

Functions
INLINE AntisymmetricTensor	antisymmetricOuter (const Vector &v1, const Vector &v2)
INLINE bool	almostEqual (const AntisymmetricTensor &t1, const AntisymmetricTensor &t2, const Float eps=EPS)
	Checks if two tensors are equal to some given accuracy. More...
template<>
INLINE Float	norm (const AntisymmetricTensor &t)
template<>
INLINE Float	normSqr (const AntisymmetricTensor &t)
	Arbitrary squared norm of the tensor. More...
template<>
INLINE auto	abs (const AntisymmetricTensor &t)
	Returns the tensor of absolute values. Resulting tensor is necessarily symmetric. More...
template<>
INLINE Float	minElement (const AntisymmetricTensor &t)
	Returns the minimal element of the tensor. More...
template<>
INLINE AntisymmetricTensor	min (const AntisymmetricTensor &t1, const AntisymmetricTensor &t2)
	Component-wise minimum of two tensors. More...
template<>
INLINE AntisymmetricTensor	max (const AntisymmetricTensor &t1, const AntisymmetricTensor &t2)
	Component-wise maximum of two tensors. More...
template<>
INLINE AntisymmetricTensor	clamp (const AntisymmetricTensor &t, const Interval &range)
	Clamping all components by range. More...
template<>
INLINE bool	isReal (const AntisymmetricTensor &t)
template<>
INLINE auto	less (const AntisymmetricTensor &t1, const AntisymmetricTensor &t2)
INLINE Float	ddot (const AntisymmetricTensor &t1, const AntisymmetricTensor &t2)
	Double-dot product t1 : t2 = sum_ij t1_ij t2_ij. More...

Variables
const PseudoVectorTag	PSEUDOVECTOR

Detailed Description

Basic algebra for antisymmetric 2nd order tensors.

Author

Pavel Sevecek (sevecek at sirrah.troja.mff.cuni.cz)

Date

2016-2021

Definition in file AntisymmetricTensor.h.

Function Documentation

abs()

template<>

INLINE auto abs

(

const AntisymmetricTensor &

t

)

Returns the tensor of absolute values. Resulting tensor is necessarily symmetric.

Definition at line 158 of file AntisymmetricTensor.h.

almostEqual()

INLINE bool almostEqual	(	const AntisymmetricTensor &	t1,
		const AntisymmetricTensor &	t2,
		const Float	eps = EPS
	)

Checks if two tensors are equal to some given accuracy.

Definition at line 139 of file AntisymmetricTensor.h.

antisymmetricOuter()

INLINE AntisymmetricTensor antisymmetricOuter	(	const Vector &	v1,
		const Vector &	v2
	)

ANTISYMMETRIZED outer product of two vectors (simple outer product is not necessarily antisymmetric matrix).

Todo:

optimize

Definition at line 130 of file AntisymmetricTensor.h.

clamp()

template<>

INLINE AntisymmetricTensor clamp	(	const AntisymmetricTensor &	t,
		const Interval &	range
	)

Clamping all components by range.

Definition at line 182 of file AntisymmetricTensor.h.

ddot()

INLINE Float ddot	(	const AntisymmetricTensor &	t1,
		const AntisymmetricTensor &	t2
	)

Double-dot product t1 : t2 = sum_ij t1_ij t2_ij.

Definition at line 199 of file AntisymmetricTensor.h.

isReal()

template<>

INLINE bool isReal

(

const AntisymmetricTensor &

t

)

Definition at line 189 of file AntisymmetricTensor.h.

less()

template<>

INLINE auto less	(	const AntisymmetricTensor &	t1,
		const AntisymmetricTensor &	t2
	)

Definition at line 194 of file AntisymmetricTensor.h.

max()

template<>

INLINE AntisymmetricTensor max	(	const AntisymmetricTensor &	t1,
		const AntisymmetricTensor &	t2
	)

Component-wise maximum of two tensors.

Definition at line 176 of file AntisymmetricTensor.h.

min()

template<>

INLINE AntisymmetricTensor min	(	const AntisymmetricTensor &	t1,
		const AntisymmetricTensor &	t2
	)

Component-wise minimum of two tensors.

Definition at line 170 of file AntisymmetricTensor.h.

minElement()

template<>

INLINE Float minElement

(

const AntisymmetricTensor &

t

)

Returns the minimal element of the tensor.

Definition at line 164 of file AntisymmetricTensor.h.

norm()

template<>

INLINE Float norm

(

const AntisymmetricTensor &

t

)

Arbitrary norm of the tensor.

Todo:

Use some well-defined norm instead? (spectral norm, L1 or L2 norm, ...)

Definition at line 146 of file AntisymmetricTensor.h.

normSqr()

template<>

INLINE Float normSqr

(

const AntisymmetricTensor &

t

)

Arbitrary squared norm of the tensor.

Definition at line 152 of file AntisymmetricTensor.h.

Variable Documentation

PSEUDOVECTOR

const PseudoVectorTag PSEUDOVECTOR

Definition at line 16 of file AntisymmetricTensor.h.